Unique Rectangle Type 3

Also called UR Type 3, UR3.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

This technique assumes the puzzle has exactly one solution. It reasons about what would create a second solution, so it is only valid on a properly constructed puzzle. Do not use it to check whether a grid is well formed.

What it means

Two corners hold the pair. The other two hold extras. Those extras team up with nearby squares to make a small locked group. That group then clears its numbers out of the rest of the row, column or box.

The exact rule, for stronger players

The rule, stated exactly: Two cells hold exactly {x,y} and the other two hold {x,y} plus different extras. The extras form a virtual cell which combines with other cells in a shared house to make a naked subset.

What it removes: Apply the resulting naked subset elimination in the shared house.

Why it works: One of the two cells with extras must take an extra, so the union of extras behaves as a single cell that must hold one of them. That pseudo-cell participates in subset logic normally. This technique is only valid when the puzzle is known to have exactly one solution. It is not a deduction about Sudoku rules, it is a deduction about the puzzle setter's promise. On a grid with multiple solutions it produces wrong answers.

Worked examples

None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.

Learn these first

Unique Rectangle Type 2Two corners hold only the pair.
Naked Subset (general form)Find some squares in one row, column or box.

Related uniqueness

Unique Rectangle Type 4Two corners hold only the pair.
Unique Rectangle Type 5Like Type 2, but the extra number sits in corners that sit across from each other rather than side by side.
Unique Rectangle Type 6Like Type 4, but the two numbers form an X across the rectangle instead of sitting along one side.
Unique Rectangle with Missing CandidatesA rectangle where one corner has already lost one of the two numbers.
Avoidable RectangleFour squares can form a rectangle across two boxes.

How often does it come up?

Our rough estimate: moderately common, and the hardest UR type to see because it requires combining with a subset.

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